Finance Chapter: Present and Future Value

Study Notes

Present value (PV) of future cash flows is lower than a similar amount today due to the discounting effect.
Lump sum investments today yield higher future values due to compound interest over time.
A regular annuity refers to payments made at the end of a period, while an annuity due involves payments at the beginning, providing higher overall value due to earlier compounding.

The rate of return measures compensation for an investment, adjusted for inflation to reflect purchasing power over time.
Not accounting for inflation diminishes dollar purchasing power, affecting future expenditure planning.
The internal rate of return (IRR) assesses profitability by factoring in cash inflows and outflows over time.

Future Value (FV) can be calculated using the formula: FV = Cash Flow x (1 + interest rate) ^ number of periods.
The Rule of 72 provides a quick estimate for how long an investment will take to double based on its annual return rate.

Payments due at the end of a period are termed a regular annuity, while those at the start are called an annuity due.
Example of payments: Contributions toward retirement can be structured as annuity dues if made at the start of the year.

Present Value of 20,000in6yearsatan820,000 in 6 years at an 8% discount rate is approximately 20,000in6yearsatan812,603.
Future Value of an 18,000investmentata618,000 investment at a 6% interest rate over 7 years is approximately 18,000investmentata627,065.
By saving 3,000annuallyfor16yearsata93,000 annually for 16 years at a 9% interest rate, one could accumulate about 3,000annuallyfor16yearsata999,010 by the end.

To assess value, Todd considers an investment yielding 1,500annuallyfor40yearswitharequiredreturnof111,500 annually for 40 years with a required return of 11%, leading to a present value of approximately 1,500annuallyfor40yearswitharequiredreturnof1113,427.
Ann's annuity of 20,000forlifestartingatage55costs20,000 for life starting at age 55 costs 20,000forlifestartingatage55costs180,000; the rate of return is roughly 10.5%, highlighting the longevity of investments.

To achieve 60,000bysaving60,000 by saving 60,000bysaving2,000 annually at a 6% interest rate, it would take about 18 years.
Annual payments to pay off a 50,000debtover4yearsat1250,000 debt over 4 years at 12% interest are approximately 50,000debtover4yearsat1216,462.

A 10,000investmentat1210,000 investment at 12% interest would yield 10,000investmentat1211,200 with annual compounding and 11,268.25withmonthlycompounding,resultingina11,268.25 with monthly compounding, resulting in a 11,268.25withmonthlycompounding,resultingina68.25 difference favoring monthly compounding.